To determine the relative contributions of rods, cones, and melanopsin to pupil responses with the phase paradigm, we tested the hypothesis that the inner and outer retinal photoreceptor contributions to the pupil light reflex at mesopic and photopic light levels were combined linearly in ipRGCs as vectorial summation. The rationale for this hypothesis is that, for a fixed frequency, any sinusoidal signal (
Fig. 2A) can be represented as a vector in a polar plot (
Fig. 2B), in which the vector length represents the amplitude and the vector angle represents the phase. If the rod, cone, and melanopsin contributions are combined in the ipRGC signal to the pupil control pathways as a vector sum of their inputs, we can estimate the relative contributions of rods, cones, and melanopsin by modeling the pupil response amplitude and phase simultaneously (
Fig. 2C). We expect that for light levels below melanopsin threshold, only rods and cones contribute to the pupil response. If rod signals dominate cone signals at low mesopic light levels, the pupil amplitude should be independent of the phase of the cone signal and a flat amplitude response curve would be observed due to minimal cone contribution (
Fig. 2C). With increasing light level, cone contributions will increase and we predict a V-shape amplitude response as a function of cone modulation phase with the minimum value indicating the phase of the rod-cone cancellation. For light levels above melanopsin threshold (0 log cd/m
2), melanopsin contributions will alter this predicted pupil response pattern. Previous studies have suggested that with pulsed stimuli, a linear summation mechanism can explain the M- and L-cone interaction in pupil responses.
30,31 However, a “winner-takes-all” mechanism was postulated to explain the relative contributions of rods, cones, and melanopsin to the PLR tonic state.
13,14 In this case, the data should follow the rod, cone, or melanopsin prediction according to the light level (
Fig. 2C).